Growing legumes from cuttings

An Experiment.
One of my broad bean seedlings had snapped its stem so I've put the broken off part in water to see whether it will root - and, of course, whether the rooted bean will throw up more shoots. 
I'm confident of the latter but not about the "cutting". 
If it works, it may be a way to multiply plants without using more seeds?

I would only think it worth chopping seedlings up if they were valuable as, for me, it would be just extra time and effort for very little gain. If you saved your own broad bean seeds, the odd casualty would be better put in Mr. Greedy the composter.
Having said that, I just potted up a seed potato sprout that i knocked off a couple of days ago to see if it would root but to me they are more valuable. If it grows, I'll see what the yield is per sprout.
I remember reading about cucumbers being able to be re-rooted it the roots rot on the seedling - just after I had binned an F1 female one with only 4 seeds to the packet.

I've grown potato sprouts after I found some really long chits on some spuds. They did grow into spuds - but they were pea sized.
Cucumbers and courgettes are OK, and tomato side shoots and tops.
I'm the sort of person who keeps a jar of water on the windowsill/GH purely for sticking odd bits of plant in - also a few buckets of water lying round the garden for the prunings that I can't bear to bin.
Nothing to lose and everything to gain.